Incorporating Runs Rules into Hotelling's χ2 Control Charts

This paper illustrates a simple and effective method of incorporating runs rules into Hotelling χ2 control charts. A Markov chain will be used to obtain a desired in-control average run length (ARL). Comparisons between the basic multivariate χ2 control chart and the multivariate χ2 control chart, which incorporates the various runs rules, are based on their respective ARL performances. All multivariate χ2 control charts that incorporate the various runs rules have shown better ARL performance compared to the basic multivariate χ2 control chart for small shifts in distance λ from the in-control mean vector μ0 to the out-of-control mean vector μ s . An example of the application, based on the proposed method, is also given.